The results on trails avoiding forbidden transitions immediately follow from the
properties of \(L_{EC}(G)\)  together with the known results on PC paths. For this
specific purpose one can also use a variant \(L_{PM}(G)\)  defined using perfect
matchings (def:lpm). As will be explained in the journal version
of [1]}, this \(L_{PM}\)  construction is at work implicitly
Retoré's paper [2]}, and indeed, it is by attempting to
understand and generalize Retoré's reduction from proof nets to perfect
matchings that we were led to define the edge-colored line graph – although it
could undoubtedly have been discovered without this inspiration, since it seems
to be a rather natural construction.
